Solve sqrt{17.01/36.45}

$$\sqrt{ \frac{ 17.01 }{ 36.45 } }$$

Evaluate

$$\frac{\sqrt{105}}{15}\approx 0.683130051$$

Solution Steps

Expand \frac{17.01}{36.45} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1701}{3645}}$$

Reduce the fraction \frac{1701}{3645} to lowest terms by extracting and canceling out 243.

$$\sqrt{\frac{7}{15}}$$

Rewrite the square root of the division \sqrt{\frac{7}{15}} as the division of square roots \frac{\sqrt{7}}{\sqrt{15}}.

$$\frac{\sqrt{7}}{\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{7}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{7}\sqrt{15}}{15}$$

To multiply \sqrt{7} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{105}}{15}$$